How would you like it if your wife picked YOUR shotgun?
I'm 5'6" tall, right handed man, stocky build, short arms. At 4'11, very few shotguns will come close to fitting her right out of the box. It will be a leap of faith.
Silver's formula is generally close:
"
Ballpark LOP In Inches = 0.15(Height In Inches) + 4
(or alternately, and 'perhaps' better)
Ballpark LOP In Inches = 0.1485(Maximum outstretched arm reach from fingertip to fingertip in inches) + 4
"
She is 4'11" or 59" tall. Her LOP will be about 12.85 inches (12 7/8" in Freedom Units).
Problems with the Franchi Infinity Catalyst:
1. You can't buy replacement recoil pads. No one has them. Sold out.
2. She needs about 1 inch removed from the Length of Pull. The TSA pad and Monte Carlo stock may be a very bad combination for her gunsmith. Trying to cut over an inch of wood cut from the back of the wood could result in a very wrong looking stock. With a straight stock, just cut the wood off and install a normal butt pad do fit.
3. Recoil semi auto offers all the fuss of a semi-auto while kicking like a light weight over and under. She wants a gas semi.
4. The Benelli 20 gauge Compact is exactly the same gun, with a nicer polish and the TSA recoil pad cut off.
The LOP is 12 1/2 inches with a straight stock. That might work for her, we estimated 12 7/8"
Weight: 5.4 pounds. It will beat her shoulder like Thor's hammer. It needs about a pound and a quarter of lead.
24" barrel is fine for her, proportionally. As the stock gets shorter, the barrel has to shorten, or the gun goes muzzle heavy.
Being a semi auto, it can be shimmed for a left hander.
5. $$$$ No matter how you do it, you either pay Benelli to take the stupid TSA recoil pad off the Franchi, or you pay a gunsmith to cut it off the Franchi yourself.
There is nothing you can do about the recoil system. It's what Benellis and Franchi sell. Light weight and kicks like a mule.
If you must buy, and can't find something used that is close to her fit,
I'd buy a 20 gauge Tristar Viper G2 Compact or Mossberg Sa-20 Bantam. BOTH should have wood stocks. They are the same gun, different importers. The Tristar might be 1/8" too long, the Mossberg might be 1/8" too short. Both are SOFT SHOOTING gas recoil operating systems. Both have the 24" barrel she wants.
As the stock gets shorter, the effect of cast and drop shims diminishes, because ... angles. She might need to use the maximum cast shim, customized with a bit of metal tape cleverly installed in a stairstep pattern to increase the angle more. But that's not expensive stuff.
Bottom line: have HER shoulder the Tristar or Mossberg. They are going to weigh a bit over 6.25 pounds. Based on weight, they will kick less than the Benelli. Add in the gas recoil effect, they will kick A LOT less.
People say that gun fit isn't all that important. Try this: swap shoes with your wife then go for a 4 mile hike. She'll tell you shoe fit isn't all that important, just add lots of socks and maybe some newspaper in the toes. You? Your feet will be bloody. It's the same for a small person trying to shoot a gun that's too big... it doesn't work.
The SKB guns were mentioned, too. If you can get your hands on one, have her shoulder one! A heavy 20 gauge that fits will be softer shooting than a 5.2 pound Benelli or Franchi. And they look cool.